Knowledge Bank

As far as the behavior of the long wavelength optic phonons are concerned, there seem to exist two types of mixed crystals. In one class of mixed systems, termed here as the one-mode'' behavior type, each of the $k \sim O$ optic mode frequency varies continuously and approximately linearly with concentration from the frequency characteristic of one end member to that of the other end member. Furthermore, the strength of the mode remains approximately constant. In the other class termed here the two-mode'' type of mixed crystals, two phonon frequencies for each of the allowed optic mode of the pure crystal are observed to occur at frequencies close to those of the end members. In addition, the strength of each phonon mode of the mixed crystal is approximately proportional to the mole fraction of the component it represents. The classification of mixed crystals into two behavior types will be illustrated by a large number of examples. Various criteria so far proposed to determine the behavior type of a given mixed crystal system will be reviewed. A criterion will be proposed, which is derived from a modified random element isodisplacement model. It is found that in a crystal $ABxC1-x$, the inequality where $mB$ is the mass of atom B and $\mu AC$ the reduced mass per unit cell of AC, determines the behavior. The crystals belonging to the two-mode behavior type obey this inequality whereas it is not obeyed by the mixed crystals of the other behavior type.